The 17-year-old is currently on the books at Las Palmas, but Barcelona have already agreed a £4.5m deal to bring him to Camp Nou at the end of the season.
Should manager Quique Setien deem that Pedri is not yet ready to compete for a first-team place then it is expected that Barcelona could send him back to Las Palmas on loan for the 2020-21 campaign.
However, Marca reports that Ajax are ready to rival Las Palmas for his temporary signature and could hijack the deal when the transfer window reopens.
Barcelona enjoy a good relationship with Ajax, and the Dutch outfit's track record for developing young players is likely to make them the preferred destination for Pedri.
The teenage winger has scored three goals and created four more in 26 Segunda Division matches this season.